Estimates for torsional rigidity of convex domain via new geometric characteristics

Abstract

We introduce new geometric characteristics of a convex domain with finite boundary length and provide an algorithm for calculating them. A series of isoperimetric inequalities between new functionals and known integral characteristics of the domain are proved. Some of the inequalities have a wide class of extremal domains. We consider applications of new characteristics to the problem on estimating the torsional rigidity of a convex domain.